Assuming you don't see related errors in the javascript console, the problem will be either because you have hit a rate limit (150req/hr per source IP) or because the favorites API endpoint is returning empty results -- this occasionally seems to happen, just like it does for the search endpoint, due to backend issues at Twitter. Often the timeline API will work very reliably, while the other "minor" APIs have issues.

Experiencing this aswell. Console reports 404 on the url called from within jQuery http://api.twitter.com/favorites/damonsk.json?page=1&count=10&callback=jQuery1640743424596497789_1350632538124&_=1350632557894